The displacement x of a particle varies with time t as x=a e^ -a t +B^ β x , where a, b, α and β are positive constants. The velocity of the particle will:

Correct answer: D. go on increasing with time From question aligned & x=a e^ -α t +b e^ & V=(d x)/(d t)=-a ^ -x t +b β_e^ B+ & V=-a ^ -t +b β ^ β t aligned Velocity will decrease for certain value of t .

NEET 2005

Exam: NEET
Year: 2005
Subject: Physics
Chapter: Motion in One Dimension

NEET 2005 · Physics · Motion in One Dimension

The displacement x of a particle varies with time t as x=a e^ -a t...

The displacement

x

of a particle varies with time

t

x=a e^{-a t}+B^{\beta x}

, where

a, b, \alpha

and

\beta

are positive constants. The velocity of the particle will:

Options

Abe independent of $\beta$
Bdrop to zero when $\alpha=\beta$
Cgo on decreasing with time
Dgo on increasing with time

Correct answer

D. go on increasing with time

Step-by-step solution

From question

\begin{aligned}& x=a e^{-\alpha \mathrm{t}}+b e^{\betat} \\ & V=\frac{d x}{d t}=-a \alphae^{-x t}+b \beta_e^{\mathrm{B}+} \\ & \Rightarrow \mathrm{V}=-a \alphae^{-t}+b \beta \varepsilon^{\beta t} \end{aligned}

\therefore

Velocity will decrease for certain value of

t$.

Practice Motion in One Dimension on Quantrex Academy →

More from Motion in One Dimension

A vehicle runs on a straight road of length 'L'. It travels half the distance with speed… MHT CET Medical 2026 For uniform acceleration in linear motion which of the following is NOT CORRECT ? MHT CET Medical 2026 Two cars, P and Q move toward each other, getting 8\ m closer every second. If they move… MHT CET Medical 2026 A block is kept on the floor of an elevator at rest. The elevator starts descending with… MHT CET Medical 2026 The acceleration (a ) -time (t ) graph for the body starting from rest is as shown in the… MHT CET Medical 2026 A train accelerates from rest at a constant rate 'p' for some time (attains velocity 'v')… MHT CET Medical 2026 The following plots show variation of velocity ( v ) with time ( t ), of a ball thrown… NEET 2026 Consider a particle moving along a straight line, whose position as a function of time is… NEET 2026 Full Motion in One Dimension list All NEET PYQs